ThmDex – An index of mathematical definitions, results, and conjectures.
Difference of set and finite union equals intersection of differences
Formulation 0
Let $X, E_1, \ldots, E_N$ each be a D11: Set.
Then \begin{equation} X \setminus \bigcup_{n = 1}^N E_n = \bigcap_{n = 1}^N (X \setminus E_n) \end{equation}
Formulation 1
Let $X, E_1, \ldots, E_N$ each be a D11: Set.
Then \begin{equation} X \setminus (E_1 \cup \cdots \cup E_N) = (X \setminus E_1) \cap \cdots \cap (X \setminus E_N) \end{equation}
Subresults
R4173: Difference of set and binary union equals intersection of differences
Proofs
Proof 0
Let $X, E_1, \ldots, E_N$ each be a D11: Set.